%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP133-2.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:28:05 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of formulae : 83 ( 23 unt; 0 def)
% Number of atoms : 198 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 180 ( 65 ~; 115 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 61 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(no_redundancy,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ greater(VAR_1,VAR_2)
| ~ next(VAR_0,VAR_2)
| ~ product(VAR_0,e_1,VAR_1) ),
file('theBenchmark.p',no_redundancy) ).
cnf(c_1,plain,
( ~ greater(B,C)
| ~ next(A,C)
| ~ product(A,e_1,B) ),
inference(clausify,[status(thm)],[no_redundancy]) ).
fof(e_1_then_e_2,axiom,
next(e_1,e_2),
file('theBenchmark.p',e_1_then_e_2) ).
cnf(c_3,plain,
next(e_1,e_2),
inference(clausify,[status(thm)],[e_1_then_e_2]) ).
fof(e_3_greater_e_2,axiom,
greater(e_3,e_2),
file('theBenchmark.p',e_3_greater_e_2) ).
cnf(c_4,plain,
greater(e_3,e_2),
inference(clausify,[status(thm)],[e_3_greater_e_2]) ).
cnf(c_6,plain,
( ~ greater(A,e_2)
| ~ product(e_1,e_1,A) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(product_total_function2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_2,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_total_function2) ).
cnf(c_9,plain,
( equalish(C,D)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_total_function2]) ).
fof(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('theBenchmark.p',e_3_is_not_e_1) ).
cnf(c_11,plain,
~ equalish(e_3,e_1),
inference(clausify,[status(thm)],[e_3_is_not_e_1]) ).
fof(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_13,plain,
~ equalish(e_2,e_1),
inference(clausify,[status(thm)],[e_2_is_not_e_1]) ).
fof(product_right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_1,VAR_3)
| ~ product(VAR_0,VAR_3,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_right_cancellation) ).
cnf(c_16,plain,
( equalish(B,D)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_right_cancellation]) ).
fof(product_left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_0,VAR_3)
| ~ product(VAR_3,VAR_1,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_left_cancellation) ).
cnf(c_17,plain,
( equalish(A,D)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
cnf(c_19,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_17,c_11]) ).
cnf(c_22,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_16,c_11]) ).
cnf(c_24,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolve,[status(thm)],[c_9,c_13]) ).
cnf(c_25,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_3) ),
inference(resolve,[status(thm)],[c_9,c_11]) ).
fof(qg3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_2,VAR_3,VAR_0)
| ~ product(VAR_1,VAR_0,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3) ).
cnf(c_27,plain,
( product(C,D,A)
| ~ product(B,A,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg3]) ).
fof(product_total_function1,axiom,
! [VAR_0,VAR_1] :
( product(VAR_0,VAR_1,e_3)
| product(VAR_0,VAR_1,e_2)
| product(VAR_0,VAR_1,e_1)
| ~ group_element(VAR_1)
| ~ group_element(VAR_0) ),
file('theBenchmark.p',product_total_function1) ).
cnf(c_28,plain,
( product(A,B,e_3)
| product(A,B,e_2)
| product(A,B,e_1)
| ~ group_element(B)
| ~ group_element(A) ),
inference(clausify,[status(thm)],[product_total_function1]) ).
fof(element_3,axiom,
group_element(e_3),
file('theBenchmark.p',element_3) ).
cnf(c_29,plain,
group_element(e_3),
inference(clausify,[status(thm)],[element_3]) ).
fof(element_1,axiom,
group_element(e_1),
file('theBenchmark.p',element_1) ).
cnf(c_31,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_32,plain,
~ product(e_1,e_1,e_3),
inference(resolve,[status(thm)],[c_4,c_6]) ).
cnf(c_33,plain,
( product(B,B,A)
| ~ product(A,A,B) ),
inference(factor,[status(thm)],[c_27]) ).
cnf(c_310,plain,
( product(e_3,A,e_3)
| product(e_3,A,e_2)
| product(e_3,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_28,c_29]) ).
cnf(c_37,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_310,c_29]) ).
cnf(c_311,plain,
( product(e_1,A,e_3)
| product(e_1,A,e_2)
| product(e_1,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_28,c_31]) ).
cnf(c_312,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_311,c_31]) ).
cnf(c_45,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_32,c_312]) ).
cnf(c_313,plain,
( product(e_3,A,e_3)
| product(e_3,A,e_2)
| product(e_3,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_28,c_29]) ).
cnf(c_47,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_313,c_31]) ).
cnf(c_314,plain,
( product(e_1,A,e_3)
| product(e_1,A,e_2)
| product(e_1,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_28,c_31]) ).
cnf(c_49,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_314,c_29]) ).
cnf(c_50,plain,
~ product(e_3,e_3,e_1),
inference(resolve,[status(thm)],[c_33,c_32]) ).
cnf(c_51,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(resolve,[status(thm)],[c_50,c_37]) ).
cnf(c_52,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_45,c_33]) ).
cnf(c_58,plain,
( ~ product(e_3,e_1,e_3)
| product(e_3,e_3,e_2) ),
inference(resolve,[status(thm)],[c_51,c_22]) ).
cnf(c_60,plain,
( ~ product(e_1,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(resolve,[status(thm)],[c_51,c_19]) ).
cnf(c_62,plain,
( product(e_1,A,e_2)
| ~ product(e_2,e_2,A)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_52,c_27]) ).
cnf(c_89,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_47,c_58]) ).
cnf(c_101,plain,
( product(e_3,e_3,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_49,c_60]) ).
cnf(c_315,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,A,e_1)
| ~ product(e_3,e_1,A) ),
inference(resolve,[status(thm)],[c_27,c_49]) ).
cnf(c_316,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_315,c_47]) ).
cnf(c_106,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_50,c_316]) ).
cnf(c_127,plain,
( product(e_2,e_2,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_89,c_33]) ).
cnf(c_132,plain,
( ~ product(e_1,e_3,e_2)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_89,c_19]) ).
cnf(c_133,plain,
( product(e_2,e_2,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_101,c_33]) ).
cnf(c_137,plain,
( ~ product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_101,c_22]) ).
cnf(c_317,plain,
( product(e_2,e_2,e_3)
| product(e_3,e_1,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(resolve,[status(thm)],[c_19,c_127]) ).
cnf(c_157,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_317,c_45]) ).
cnf(c_318,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_133,c_62]) ).
cnf(c_160,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_318]) ).
cnf(c_319,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(resolve,[status(thm)],[c_22,c_160]) ).
cnf(c_320,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_319,c_45]) ).
cnf(c_194,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_320]) ).
cnf(c_321,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_2,e_3)
| product(e_1,A,e_3)
| ~ product(e_1,e_3,A) ),
inference(resolve,[status(thm)],[c_27,c_157]) ).
cnf(c_322,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_2,e_2,e_3)
| product(e_1,e_1,e_3) ),
inference(resolve,[status(thm)],[c_321,c_194]) ).
cnf(c_323,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_2,e_3)
| product(e_1,e_1,e_3) ),
inference(copy,[status(thm)],[c_322]) ).
cnf(c_197,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_2,e_3) ),
inference(resolve,[status(thm)],[c_32,c_323]) ).
cnf(c_324,plain,
( product(e_1,e_1,e_1)
| ~ product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_25,c_197]) ).
cnf(c_325,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_324,c_52]) ).
cnf(c_210,plain,
product(e_1,e_1,e_1),
inference(copy,[status(thm)],[c_325]) ).
cnf(c_213,plain,
~ product(e_1,e_1,e_2),
inference(resolve,[status(thm)],[c_24,c_210]) ).
cnf(c_214,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_22,c_210]) ).
cnf(c_216,plain,
~ product(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_19,c_210]) ).
cnf(c_226,plain,
( ~ product(e_3,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_214,c_137]) ).
cnf(c_326,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_214,c_106]) ).
cnf(c_233,plain,
( product(e_3,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_216,c_326]) ).
cnf(c_253,plain,
( ~ product(e_1,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_216,c_132]) ).
cnf(c_271,plain,
~ product(e_2,e_2,e_1),
inference(resolve,[status(thm)],[c_33,c_213]) ).
cnf(c_327,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_233,c_226]) ).
cnf(c_300,plain,
product(e_1,e_3,e_2),
inference(copy,[status(thm)],[c_327]) ).
cnf(c_302,plain,
product(e_3,e_1,e_2),
inference(resolve,[status(thm)],[c_300,c_253]) ).
cnf(c_328,plain,
( product(e_2,A,e_1)
| ~ product(e_3,e_1,A) ),
inference(resolve,[status(thm)],[c_27,c_300]) ).
cnf(c_329,plain,
~ product(e_3,e_1,e_2),
inference(resolve,[status(thm)],[c_328,c_271]) ).
cnf(c_309,plain,
$false,
inference(resolve,[status(thm)],[c_302,c_329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP133-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n003.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 14:32:24 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 383943 was started by sandbox on n003,
% 0.17/0.45 % Fri Sep 25 14:32:24 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.50
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.50
% 0.17/0.50 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.17/0.50 % Length of proof is 51.
% 0.17/0.50 % Level of proof is 16.
% 0.17/0.50 % Maximum clause weight is 21.000.
% 0.17/0.50 % Given clauses 126.
% 0.17/0.50
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------